What is the least common multiple of 16 and 24?

2 Answers
Mar 24, 2018

The lowest common multiple (LCM) of 1616 and 2424 is 4848.

Explanation:

The prime factorization of 1616:
16 = 2*2*2*2 = 2^416=2222=24

The prime factorization of 2424:
24 = 2 * 2 * 2 *3 = 2^3*324=2223=233

Both 1616 and 2424 have 2^323 (88) in common, so we can remove it from one of the numbers, leaving 2^424 and 33. There are no more numbers in common, so the lowest common multiple is 2^4 * 3 = 48243=48.

Mar 24, 2018

A very different way of thinking about it!

48

Explanation:

Think of 16 as 16/24->8/12->4/6->2/316248124623 of 24

2/3->23 Not a whole number

2/3+2/3->4/323+2343 Not a whole number

2/3+2/3+2/3=6/3->23+23+23=63 whole number of 2

2xx24=482×24=48
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color(blue)("Why does this work?")Why does this work?

Although it is not obvious the above process is linked to what follows.

16 is a portion of 24 in that 16+8=2416+8=24

So we cycle through occurrences of 16+816+8 until we have values such that 1616 will divide exactly into the sum of the 8's. The 8's being part of the 24 means we are counting the 24's.

16+8 = 2416+8=24
ul(16+8=24)
32+16=48

Within the 48 is another complete 16. In that we now have 3 lots of 16.